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Elvira Kent (Janis Paige) and her husband Michael (Don DeFore) suspect each other of cheating. For their wedding anniversary, Elvira books an ocean cruise to Rio de Janeiro but her husband claims that unexpected business will prevent him from going. Seeing an opportunity, Elvira pretends to take the trip alone, but in fact sends singer Georgia Garrett (Doris Day), a woman she'd met at the travel agency, in her place and under her name. By secretly staying behind, Elvira hopes to find out if Michael is indeed sneaking around behind her back. Michael, however, is suspicious over Elvira's supposed willingness to go on the trip alone, and so hires private detective Peter Virgil (Jack Carson) to see if she is sneaking around behind his back.

Peter joins the cruise and, as part of his job, becomes acquainted with Georgia. Georgia, following the instructions of the real Elvira, keeps up the ruse by pretending to be Elvira to everyone, including Peter. Georgia and Peter are attracted to each other and gradually fall in love, which causes conflict for both of them.

During one of the cruise stops, Georgia's friend, Oscar Farrar (Oscar Levant), comes on board. Oscar is in love with Georgia despite Georgia's lack of interest in him, and when Peter spots them together, he thinks he has discovered the identity of Elvira's lover.

The film's third act is set in a Rio hotel, where all the principal characters converge and ride a merry-go-round of mistaken identities. Sorting out their true identities, resolving the crossed love plots, concludes the picture.

Originally conceived as a star vehicle for Betty Hutton, the film had to be recast when Hutton became pregnant, and thus unavailable. Other established stars like Judy Garland and Jane Powell were briefly considered, before Michael Curtiz was talked into auditioning Doris Day, a well-known band vocalist, but hitherto not considered an actress. Her personal life was in some turmoil at the time, as her second marriage, to musician George Weidler, was ending, and this, combined with her evident nervousness, led her to deliver a notably teary, emotive version of Embraceable You at the audition. Impressed by her singing ability and fresh-faced good looks, Curtiz signed her to a film contract and cast her in the leading role of Georgia Garrett. Despite the change in star and the late casting of Janis Paige, the film was financially successful.